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Neher-McGrath Ductbank heating, RHO value, Cable Ampacity

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Rho Value of Dirt

Cable Ampacity Resistance Table

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Cable Temperature Rise Calculation

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Cable Temperature Rise Calculation Underground Cables Ratings Calculation
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INCREASING THE AMPACITY OF UNDERGROUND CABLES 6.1 Overview Once there is an understanding of the possible limitations associated with each cable type, it is necessary to consider how uprating might occur on a given circuit. This report section describes various techniques that may be applied to investigate ampacity limitations and then ways to improve ampacity, or at least have a better understanding of what is limiting the ampacity. 6.2 Route Thermal Survey A route thermal survey is traditionally involved evaluating the entire cable route in a detailed manner to understand ampacity limitations. Many North American utilities adhere to Association of Edison Illuminating (AEIC) standards regarding cable design. One of the principles of these standards is that if the soil characteristics are not well known, the design ampacity should be based upon a maximum operating temperature that is 10C below the allowable operating temperature (e.g., values in Table 4-8). Regardless of following the AEIC standards or not, utilities sometimes design cable circuits without a good knowledge of the route characteristics, particularly with older circuits. The ambient soil temperature and soil thermal resistivity were not well known, so assumed values were often incorporated into rating calculations. Those following the AEIC guidelines obtained some additional conservatism in the ratings by using the lower 10C operating temperature in the event the assumed parameters were inaccurate. However, as the circuits age and load growth continues, many utilities are revisiting the rating assumptions to see if additional transmission capacity is available without major investment in infrastructure. Also, during the process of uprating a cable circuit, hot spot mitigation may require removing existing trench backfill materials and replacing with a good quality thermal backfill. The following subsections discuss some of the techniques employed for a route thermal survey and describe soil and backfill characteristics that are important to consider in evaluating methods for uprating cable systems. "Neher-Mcgrath Calculation" "Neher-Mcgrath heating"

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Neher-Mcgrath Neher-Mcgrath Neher-Mcgrath Neher-Mcgrath Neher-Mcgrath Neher-Mcgrath IEEE 442 IEEE 442 IEEE 442 IEEE 442 442-1981 - IEEE Guide for Soil Thermal Resistivity Measurements Description: This guide covers the measurement of soil thermal resistivity. A thorough knowledge of the thermal properties of a soil will enable the user to properly install and load underground cables. The method used is based on the theory that the rate of temperature rise of a line heat source is dependent upon the thermal constants of the medium in which it is placed. The designs for both laboratory and field thermal needles are also described. The main purpose of this guide is to provide sufficient information to enable the user to select useful commercial test equipment, or to manufacture equipment which is not readily available on the market, and to make meaningful resistivity measurements with this equipment. Measurements may be made in the field or in the laboratory on soil samples or both. 6-1 6.2.1 Thermal Property Analysis In the equivalent thermal circuit, the earth thermal resistances are the largest component typically representing over 50% of the total thermal resistance. They are also the least understood. As compared with overhead lines where weather parameters (wind speed and direction, solar radiation, temperature) may be valid for a 1-2km of line length, soil characteristics along underground cable routes can vary over a few meters. If the cables are buried in city streets, there exists a strong possibility of encountering "borrowed fill" instead of native soils. These "fills" may satisfy civil/construction requirements but if topsoil, cinders or organic soils are used, the thermal performance may be very poor. For this reason, it is very important to test the soils so that appropriate values of thermal resistivity may be used in design calculations. Thermal property analysis based on transient heat flow was first suggested as early as 1888 (Wiedman, 1888). During the mid-1900s, significant research and other work was conducted in North America (Mason and Kurtz-1952, Blackwell-1954, Carslaw and Jaeger-1959). This demonstrated the practical use of a thermal needle "line heat source" method. The Insulated Conductors Committee, organized in 1947, performed a special project on soil thermal resistivity in 1951. A special subcommittee (No. 14) headed by Professor H. F. Winterkorn of Princeton University continued work in this field for 10 years and published the AIEE Committee Report in 1960. In the 1970s, EPRI-sponsored research resulted in the design and development of the Thermal Property Analyzer. The basic approach was to develop a portable, fully automated test instrument with standardized testing procedure that could be employed for both field and laboratory with results that could be extended to power cable systems. 6.2.1.1 Thermal Resistivity Thermal resistivity, sometimes call "rho", is a property of a material. In the contents of cable installation and field measurements, the thermal resistivity is measured for a soil or trench backfill. The most common approach to thermal resistivity measurements now is the "transient thermal needle" method, which is based on the "line heat source theory". Essentially, an underground cable is a long distributed heat source. The "transient thermal needle" method takes advantage of this characteristic by using a "thermal probe" which contains a heating coil throughout its length and a thermistor type temperature sensor at the mid-point of the heater. The length to diameter ratio of the probe is high enough so that end effects do not impact the measurements. An example thermal probe is shown in the following figure: Once the probe is installed in the soil sample or in the native soil (field), the heater in the thermal probe is energized with a constant power while the change in temperature is recorded over time (usually 20-30 minutes). The slope of the Log time-temperature curve is proportional to the thermal resistivity of the soil sample. A thermal property analyzer (TPA) was developed to automate this process and is commonly used for both field and laboratory measurements. The transient thermal probe method (e.g., IEEE Standard 442) is a relatively quick and accurate approach to measuring soil thermal properties provided the theoretical assumptions are understood and care is taken in the test set-up to stay within the limits of the theory. The test assumes various conditions: The probe is an instantaneous and constant heat source (no thermal capacitance) Heat flow is radial
    Conduction is the only mechanism of heat transfer There is no contact resistance at the soil/probe interface There is an infinite sample boundary The test sample is homogeneous and at moisture and thermal equilibrium No moisture migration occurs during the test

Underground Cables Need a Proper Burial Apr 1, 2003 12:00 PM By Deepak Parmar and Jan Steinmanis, Geotherm Inc. Overhead systems are out in the open, so it is easy to detect and fix design and installation problems. Underground problems, however, are out of sight and out of mind, at least until cables start failing. Although utilities design their underground circuits for a 30-year life, improper installations often can lead to premature field failures. Unless you lay your cables to rest properly, they may come back to haunt you. Here's a brief example. A wind-generating farm was installed with underground cables tied directly to a main feeder cable. Unfortunately, the cables were simply placed in a trench using native soil backfill with minimal soil compaction. Ampacity calculations were performed using typical soil values, but thermal properties were not measured. Since wind turbines operate almost continuously, the feeder cable often ran at maximum capacity. The heat generated from the feeder cable dried out the surrounding soil completely. Because the native soil was poorly compacted fine silt, it acted like an insulating blanket and the cable failed prematurely. A significant source of potential problems with underground circuits is the improper selection and installation of thermal backfill materials. To prevent premature failures, you must ensure you place cable systems in a hospitable environment. Too few utilities have stringent specifications or quality-assurance programs for installing cable-trench backfill; this often leaves the decision up to the civil contractor. The effects of poorly installed thermal backfills and soils may not be evident for many years, until cable loads increase and temperatures rise beyond allowable levels, resulting in cable failures. The remedial cost of removing and replacing poor backfills is high, especially under paved roads. The loss of revenues from derating a system may be even higher. Installing a new circuit may be the only, albeit expensive, option. Importance of Soil and Backfill All the heat generated by an underground power cable must be dissipated through the soil. This is quantified by the soil thermal resistivity (or thermal rho, C-cm/W), which can vary from 30 to 500C-cm/W. Electrical engineers understand the performance of the cable quite well, but to most, the soil behavior is a mystery, usually handled by using a thermal backfill with a supposedly "safe" thermal rho. The ability of the surrounding soil to transfer the heat determines whether an operating cable remains cool or overheats. Improving the external thermal environment and accurately defining the soil and backfill thermal rho commonly results in a 10% to 15% increase in cable ampacity, with 30% improvements noted in some cases. You can address potential problems by measuring the native soil's thermal properties and by using properly designed and installed corrective thermal backfills in the cable trench. In recent years, we've learned that using thermal probes connected to a Thermal Property Analyzer (EPRI EL-2128) can accurately measure the thermal rho in the field and laboratory. The use of a soil thermal rho of 90C-cm/W has become ingrained in cable engineering practices. Soil studies performed in the 1950s found this was a "safe" value for most moist soils. This value is commonly used for distribution cables, where cable loads are usually low and the native soil is used as the backfill. For transmission cables, it is assumed that the "thermal backfill" placed around the cables will be much better than the native soil and that it will have a thermal rho of less than 90C-cm/W. Thermal Backfills Most moist soils (with the exception of organic clays and silts, volcanic soils, peat and fills with ash and slag) have a rho of less than 90C-cm/W. Moist sands, which are commonly placed around transmission cables, may even have a rho of less than 50C-cm/W. The critical word is "moist." Many soils, especially uniform sands, can dry substantially when subjected to heat from the cables. The thermal rho of a dry soil would exceed 150C-cm/W, and possibly approach 300C-cm/W for a dry uniform sand. (The dry thermal rho of a properly designed and installed thermal backfill should be less than 100C-cm/W and possibly as low as 75C-cm/W). In fact, a contractor, if left to his or her own devices, most likely would use readily available fine sand or concrete sand as the backfill. From a construction viewpoint, this sand makes an inexpensive and excellent bedding material, but thermally, it is very poor because it dries out easily under high cable loads. Unfortunately, over the years utilities have used many unsuitable sands or "thermal backfills" because of ease of installation and availability. Several route thermal surveys of existing circuits installed before 1980 confirm this practice. Almost any sand, when moist, will give a reasonably low thermal rho. The crucial aspect is how easily it dries when subjected to cable heat loads. Soils in semi-arid climates are naturally quite dry, so the assumption of a moist soil is not valid. It doesn't take much to dry these soils completely. In many parts of the country, the soil mineral and consistency is such that there is a high intrinsic thermal rho. Soil that is not properly compacted in the cable trench will be less dense and have a substantially higher thermal rho. Even distribution or low-voltage cables that are continuously under full load may dry the soil. Cables that are near other heat sources, such as steam mains, will experience higher ambient temperatures, and if in the vicinity of other cables, will experience mutual heating and run hotter. The thermal rho is important not only for transmission cables but also in any situation resulting in high heat generation. The assumption of a soil and backfill thermal rho of 90C-cm/W may be erroneous, possibly leading to long-term problems when the cable is heavily loaded. Poorly compacted trench backfill is a major problem. Not only is the thermal rho of uncompacted soil significantly higher, but the loose soil will dry more easily, which increases the possibility of thermal runaway. Corrective Thermal Backfills Generally, native soils do not make good thermal backfills because their thermal rho values are poor, or they are difficult to properly re-compact in a cable trench. There are also problems associated with stockpiling, screening of debris, and contamination of good soil with organic topsoil. In the long run, the operational reliability gained by placing a classified thermal backfill around the cable has advantages over the variability and uncertainty of recompacted native soil. Compacted granular backfills can have good thermal properties. Since most of the heat conduction is through the soil mineral particles and their contacts, one must ensure a high-density soil mixture to maximize these contacts. A well-graded sand to fine gravel can be a good thermal backfill when compacted to its maximum density as determined by a laboratory standard Proctor test (ASTM D698). The total cost of a compacted backfill must include material and transportation costs, as well as installation labor and quality-assurance costs. The one often-neglected factor about compacted backfills is the need for quality assurance during installation. If the gradation of the backfill is not correct (sieve analysis ASTM D422), or it is not at the optimum moisture content (ASTM D698), or not enough compaction effort is applied, or the backfill lifts are too thick, then the maximum density will not be achieved and the thermal capability degraded. Cement stabilized sand frequently has been used as a cable trench backfill in many countries. A typical mix design consists of 14 parts sand to one part cement, mixed with about 8% water. If the correct sand is used and properly installed, this material can have acceptable thermal performance. However, this backfill is quite strong and thus would be difficult to excavate. Quality control is required during mixing and installation, otherwise the thermal performance cannot be assured. Many North American utilities have been using stone dust or crushed stone screenings as thermal backfill. If well graded and of the right mineral type, it provides a low and stable thermal resistivity when compacted at optimum moisture content and density. It does require thorough testing to establish density, moisture and thermal performance, and a good quality-control program to ensure proper installation. With compacted soils, maximum soil density is needed in the restricted trench areas near cables or around cable pipe groups where proper compaction is difficult. Yet, it is precisely in these zones adjacent to the cables, where the heat flux is highest, that suitable compaction is most important to ensure maximum heat dissipation from the cables. Fluidized Thermal Backfills Over the past 10 to 15 years, we've seen great acceptance of fluidized thermal backfills (FTB), which are formulated to meet thermal resistivity, thermal stability, strength and flow criteria. This free-flowing, controlled-density fill is ideal for hard-to-access areas, such as narrow trenches, small diameter tunnels or areas congested with many underground services basically where mechanical compaction is not feasible or practical. While the material cost of FTB may be higher, it should be considered for general usage because of its assured quality and quick installation, thus speeding up construction and decreasing overall costs, which are important factors when working in busy city streets. FTB is a slurry backfill consisting of medium aggregate, sand, a small amount of cement, water and a fluidizing agent. FTBs can be formulated using locally available aggregates. The component proportions are chosen by laboratory testing of trial mixes to minimize thermal resistivity and maximize flow without segregating the components. Be wary of commonly available "controlled density fills," "flowable fills" or "slurry backfills," which use large volumes of fly ash or sand. These may meet the mechanical and flow requirements for trench backfilling, but too often they provide totally unsuitable thermal performance. Fluidized thermal backfills should be formulated and tested only by soil thermal specialists who understand the tricks of the trade in making thermal measurements. Fluidized thermal backfills do not have to be compacted; they flow in a fashion similar to concrete. In fact, FTB is typically supplied from concrete trucks, and may be poured or pumped, and seldom requires any special shoring or bulkheading. It solidifies to a uniform density by consolidation, with excess water seeping to the top. Regular FTB can be pumped up to 150 m (500 ft) using conventional concrete pumping equipment and greater distances with special modifications. It hardens quickly so that the ground surface may be reinstated the next day, but the low strength (100 to 250 psi [0.7 to 1.8 MPa]) allows it to be broken up with a backhoe if required. If a higher strength is required, the cement content can be increased and the water adjusted without degrading the thermal performance. FTB will flow readily to fill all the spaces, without vibration, yet harden quickly. Future settlements are negligible. It also affords mechanical protection for the cables or cable pipes and provides support for underground and surface facilities (road pavement). FTB has good heat dissipation properties even when totally dry. Depending on the mix design, typical thermal rhos are 35 to 40C-cm/W wet, and 70 to 100C-cm/W dry, with excellent thermal stability. The FTB can be formulated for use in both flat and hilly terrain. Thicker, slower flowing mixes can be formulated when addressing an area with a significant slope. Backfills The Right Way The use of a well-designed thermal backfill can enhance the heat dissipation and increase the allowable ampacity of an underground power cable, as well as alleviating thermal instability concerns. The corrective backfill will reduce the heat flux experienced by the native soil so that it will not dry out; therefore, the stability of the native soil is no longer a concern. A good backfill should be better able to resist total drying and also have a low dry thermal rho if it is completely dried. It should be available at a reasonable cost, and be easy to install and easy to remove if required. The thermal backfill must be laboratory evaluated and include specifications for mineral quality, gradation (sieve analysis), thermal dryout curve and optimum density. Typically, the entire trench width is filled with thermal backfill to a minimum height of 300 mm (12 inches) above the cables. For poor native soil conditions or heavily loaded cables, the thickness of the backfill can be increased to maintain a low composite thermal rho. A fluidized thermal backfill is the ideal way of providing a high-quality cable backfill. Deepak Parmar is president of Geotherm Inc. From 1960 to 1978, he worked on various civil engineering (soil and rock mechanics) projects in the United Kingdom and Canada. Since forming Geotherm Inc. in 1978, Parmar has worked solely on underground and submarine power cable projects. He received the BS degree in civil engineering from Woolwich Polytechnic, United Kingdom, in 1966, and the Diploma in Management Studies (DMS) from Slough, United Kingdom, in 1972. He is a member of the Engineering Institute of Canada, Canadian Society for Civil Engineers, Canadian Geotechnical Society, Canadian Society for Electrical and Computer Engineers, Tunneling Association of Canada, IEEE/PES/ICC, Canadian Electrical Association and CIGR. Jan Steinmanis is vice president of Geotherm Inc. He received a B.A.Sc. degree in civil engineering from the University of Toronto, Canada, in 1975. From 1976 to 1982, Steinmanis worked as a research engineer with Ontario Hydro, where he worked on several civil engineering projects and on the Electric Power Research Institute (EPRI)-funded projects for the Development of Thermal Property Analyzer. He also conducted several research projects, including the soil geotechnical-thermal properties database for Canada (a Canadian government-funded project). He is a registered professional engineer. Elements of a Cable Route Thermal Survey Perform in-situ thermal rho testing and sampling of the native soils. This may be done in conjunction with any required geotechnical testing, such as for manholes. Review any available soils information so test locations cover all the soil types. In the laboratory, perform thermal dryout tests (thermal rho vs. soil moisture) on select samples. This will define the thermal rho for drier soil conditions. Source and design the fluidized thermal backfill (or compacted granular backfill) based on locally available materials. This also will include a thermal dryout curve. Choose the design thermal rho values for the native soil and thermal backfill based on the lowest expected soil moistures. Use a computer cable design program to optimize configuration of cables, trench size and thermal backfill envelope. Soil Components Description Thermal Resistivity Dry (C-cm/W) Soil Grains Quartz 12 Granite 30 Limestone 40 Sandstone 50 Shale (sound) 60 Shale (highly friable) 200 Mica 170 Others Ice 45 Water 165 Organics 500 Oil (petroleum) 800 Air 4500 Thermal Stability Thermal stability describes the ability of a moist soil to maintain a relatively constant thermal rho when subjected to a cable heat load, thus preventing a power cable from exceeding its safe operating temperature. Thermal instability (or "thermal runaway") occurs when a soil is unable to sustain the heat from a cable. The soil progressively dries, resulting in a substantial increase in the thermal rho and attendant increase in the cable-operating temperature. If soil moisture is not replenished or current reduced, the ultimate result may be a totally dry thermal rho and cable failure caused by overheating. Visually, thermal runaway can be described on a thermal dryout curve. At high moistures, the curve is relatively flat, so any minor drying of the soil will not change the thermal rho very much (thermally stable). Excessive cable heat will dry the soil below the knee of the curve (critical moisture), and the thermal rho will increase significantly. This will cause the cable to get hotter, thus drying the soil more. The thermal rho will "walk" up the thermal dryout curve as the soil dries, eventually giving a totally dry thermal rho near the cable. When Not to Worry About Thermal Stability? Thermal instability concerns can be minimized by always using a fluidized thermal backfill around the cable. The thermal dryout curve of a good backfill has a sharp knee at a low critical moisture content and the totally dry thermal rho is quite low. For these backfills the thermal stability may be treated as a binary concept, that is, if the lowest expected moisture is above the critical moisture content then the backfill is stable for normal heat rates and the moist thermal rho may be used in ampacity calculations. If the lowest expected moisture is below the critical moisture then the backfill is unstable and the totally dry thermal rho must be used for the design. For FTB, the totally dry thermal rho is usually less than 90C-cm/W, so it is still quite acceptable. By using a sufficiently large thermal backfill envelope, the heat flux through the native soil will be quite low; therefore, the native soil will not dry out, and the stability of the native soil is not a concern.

Underground Power Cable Installations: Soil Thermal Resistivity Gaylon S. Campbell Decagon Devices Inc. Pullman, WA 99163 USA Keith L. Bristow CSIRO Land and Water Davies Laboratory PMB PO Aitkenvale Townsville QLD 4814 Who would have thought that an electrical power engineer would need to be an expert at soil physics as well. But, increasingly, such knowledge is becoming critical in the design and implementation of underground power transmission and distribution systems. The issues are simple enough. Electricity flowing in a conductor generates heat. A resistance to heat flow between the cable and the ambient environment causes the cable temperature to rise. Moderate increases in temperature are within the range for which the cable was designed, but temperatures above the design temperature shorten cable life. Catastrophic failure occurs when cable temperatures become too high, as was the case in Auckland, NZ in 1998. Since the soil is in the heat flow path between the cable and the ambient depth ground surface cable installation with backfill plant cover soil environment, and therefore forms part of the thermal resistance, soil thermal properties are an important part of the overall design. The detailed calculations needed to correctly design an underground cable system have been known for over 60 years. The procedures typically used are outlined in Neher and McGrath (1957), and, more recently by the International Electrotechnical Commission (1982). These calculations can be done by hand, but most engineers now use either commercial or home-brew computer programs. The calculations are quite detailed, and are generally based on sound physics or good empiricism, until one gets to the soil. Then the numbers chosen often are almost a shot in the dark. Since, even in a well-designed system, the soil may account for half or more of the total thermal resistance, engineers need to treat that part with as much respect as they do the cables and ducts. Thermal Resistivity of Soil Good theories describing thermal resistivity of soil have been around for a long time (de Vries, 1963; Campbell and Norman, 1998). These models are based on dielectric mixing models, and treat the overall resistivity as a weighted parallel combination of the constituent resistivities. Five constituents are important in determining the thermal resistivity of soil. These are quartz, other soil minerals, water, organic matter, and air, in order of increasing resistivity. The actual values for these materials are 0.1, 0.4, 1.7, 4.0, and 40 m C/W. Without knowing anything about the weighting factors for these in an actual soil or fill material, four things should be clear: 1) Air is bad. Fill must be tightly packed to minimize air space, in order to achieve acceptably low thermal resistances. 2) Replacing air with water helps a lot, but water is still not a very good conductor. 3) Organic matter, no matter how wet, will still have a very high resistivity. 4) Fill materials high in quartz will have the lowest resistivity, other things being equal. We will illustrate some of these points with examples. Density and Thermal Resistivity Figure 1 shows how important compaction is for achieving acceptably low thermal resistivity in backfill materials. A value often assumed for thermal resistivity of soil in buried cable calculations is 0.9 m C/W. None of the curves in Fig. 1 ever get that low, even at very high density. Typical density for a field soil that can sustain plant growth is around 1.5 Mg/m3. At this density, even the quartz soil has a resistivity more than 4 times the assumed value. Three important observations can be made from Fig. 1. First, organic material is never suitable for dissipating heat from buried cable, no matter how dense. 0 2 4 6 8 10 12 14 1.2 1.4 1.6 1.8 2 2.2 Bulk Density (Mg/m3) Thermal Resistivity (m C/W) loam quartz organic Figure 1. The thermal resistivity of a dry, porous material is strongly dependent on its density. Second, thermal resistivity of dry, granular materials, even when they are compacted to extreme density, is not ideal for cable backfill. Third, the air spaces control the flow of heat, so, even though quartz minerals have 4 times lower resistivity than the loam minerals, the overall resistivity of the two are similar at similar density. It is worth mentioning that arbitrarily high densities are not attainable just by compaction. Uniform sized particles pack to a given maximum density. To attain densities beyond that, without crushing particles, smaller particles are added to the voids between the larger particles. Highest densities are therefore attained by using well-graded materials. Water Content and Thermal Resistivity Even though water resistivity is higher than that of soil minerals, it is still much lower than air. If the pore spaces in the soil are filled with water, rather than air, the resistivity decreases. Figure 2 shows the effect of water. The density is around 1.6 Mg/m3, much lower than the highest values in Fig. 1, but with a little water the resistivities are well below 1 m C/W. Now, with more water in the pores, the effect of the quartz is more pronounced. The resistivity of organic soil, though better than when dry, is still much too high to provide reasonable heat dissipation for buried cable. 0 1 2 3 4 5 6 0 0.1 0.2 0.3 0.4 Water Content (m3/m3) Thermal Resistivity (m C/W loam quartz organic Figure 2. Adding water to a porous material drastically decreases its thermal resistance. Water content in the field Since thermal resistivity varies so much with water content, and water content in soil is so variable, it is reasonable to ask what water contents to expect in field soils. Below, and even slightly above a water table the soil is saturated (all pores filled with water). In these situations, one can be certain that resistivities will remain at the lowest values possible for that soil density. Minimum water content in the root zone of growing plants typically ranges from 0.05 m3/m3 in sands to 0.1 or 0.15 m3/m3 for finer texture soils. These water contents correspond, roughly, to the water contents in Fig. 2 at which resistivity begins to increase dramatically. This is sometimes called the critical water content, and is the water content below which thermally driven vapor flow in a temperature gradient will not be re-supplied by liquid return flow through soil pores. This point is very significant in buried cable design, because, when the soil around the cable becomes this dry, the cable heat will drive the moisture away, drying the soil around the cable and increasing its resistivity. This results in additional heating, which drives away additional moisture. A thermal runaway condition can ensue. Customised backfill Lower dry resistivities than those shown in Fig. 1 can be achieved using especially designed backfill materials. A Fluidized Thermal BackfillTM (FTBTM) can be poured in place. It has a dry resistivity of around 0.75 m C/W, decreasing to below 0.5 m C/w when wet Measurement While it is possible to compute thermal properties of soil from physical properties, it is usually easier to measure them directly than to do the computations. Methods are given by ASTM(2000) and IEEE(1992). The accepted method uses a line heat source. Typically a heating wire and a temperature sensor are placed inside a small bore hypodermic needle tube with length around 30 times its diameter. Temperature is monitored while the needle is heated. In this radial heat flow system a steady state is quickly established, and one can plot temperature vs. log time to obtain a straight line relationship. The thermal resistivity is directly proportional to the slope of the line. Several companies offer instruments suitable for either field or laboratory measurements of thermal resistivity, and probes can be left in place to monitor thermal properties after the cable is installed and in use. Site-specific considerations In addition to the issues discussed above there are also several site-specific issues that need to be taken into account when designing and implementing underground power cable installations. These include trade-off analysis between depth of installation, cost of installation, and thermal stabilisation. The deeper one buries the cables the more stable the thermal environment, especially if shallow water tables and capillary upflow result in relatively moist conditions around the cables. Surface conditions will also impact on the water and energy exchange between the soil and atmosphere and hence the thermal environment around the cables. In cities the surface will more than likely be covered by roads, buildings, parks or gardens, while in rural areas bare soil or vegetative cover will be most common. It is important that surface condition and its impact on the underlying thermal environment be taken into account, and especially any change in surface condition that could result in unwanted consequences. Adding vegetation for example could result in significant soil drying, with potential consequences as discussed earlier. Clay soils in particular can crack on drying, resulting in development of air gaps around cables, and every effort must be made to avoid this happening. Potential 'hot spots' along the cable route (such as zones of well drained sandy soils or vegetated areas that could lead to significant soil drying) should receive particular attention to ensure long-term success of any installation. Conclusion There are five important points that the electrical power engineer should take from this short discussion. First, soil and backfill thermal properties must be known for a safe and successful underground power cable installation. One can't safely assume a value of 0.9 m C/W. Second, density and water content play important roles in determining what the thermal resistivity will be. Specify the density of a backfill material, and assure, through design and appropriate management that water content can't get below the critical level. Third, natural soils which support plant growth will always have much higher resistivities than engineered materials because of their lower density and variable, but sometimes low water content. Fourth, engineered backfill materials are available which can assure adequate thermal performance under all conditions. Fifth, measurement of thermal conductivity, both in the field and in the laboratory, is relatively straightforward, and should be part of any cable design and installation project. Finally, there are several site-specific issues such as depth of cable placement, vegetation and soil water management, and avoidance of excessive drying and soil cracking that could lead to air gaps, all of which need to be taken into account when designing and implementing underground power cable installations. References ASTM (2000) Standard test method for determination of thermal conductivity of soil and soft rock by thermal needle probe procedure. ASTM 5334-00 Campbell, G. S. and J. M. Norman (1998) An Introduction to Environmental Biophysics. Springer Verlag, New York. DeVries, D. A. (1963) Thermal properties of soils. in W. R. van Wijk, Physics of Plant Environment John Wiley, New York IEEE (1992) Guide for soil thermal resistivity measurements. Inst. of Electrical and Electronics Engineers, Inc. New York. International Electrotechnical Commission (1982) Calculation of continuous current ratings of cables. Publication 287, 2nd ed. Neher, J. H. and M. H. McGrath. (1957) The calculation of temperature rise and load capability of cable systems. AIEE Transactions on Power Apparatus and Systems. Vol. 76 Neher-McGrath Calculations The Neher-McGrath Calculations provide a method for calculating underground cable temperatures or ampacity ratings and are derived from the following technical paper: J. H. Neher and M. H. McGrath,"The Calculation of the Temperature Rise and Load Capability of Cable Systems", AIEE Transactions, Part III, Volume 76, pp 752-772, October, 1957. This paper considers the complicated heat transfer issues associated with the determination of underground system ampacities. The paper cites the following basic equation for calculation of a cable ampacity: However, this single equation masks the great complexity involved in these procedures. There are scores of complicated equations involved in developing the terms in this equation and those required for temperature calculations. (The paper defines over 80 variables and contains in excess of 70 formulas excluding appendices.) To solve for unique ampacities or temperatures at each cable position, a multiple set of equations must be developed to take into account interference heating from every position in the system, and a matrix solution technique for simultaneous equations utilized. AmpCalc handles all the complexity and allows the user to quickly and easily determine ampacities for virtually any underground ductbank or direct burial arrangement. Free Web Counter
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